anonymous
  • anonymous
I need help understanding integration by substitution: 63/(9x+2)^8
Mathematics
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

phi
  • phi
if you let u = 9x+2 what is du ?
xapproachesinfinity
  • xapproachesinfinity
This is the as saying f(x) =9x+2 What is f'(x) Just a difference of differentials but you don't need to worry about thst
anonymous
  • anonymous
du=9 right?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

xapproachesinfinity
  • xapproachesinfinity
Yes just one thing you missed Du=9dx
phi
  • phi
no du/dx =9 but if you "take the derivative" u= 9x you differentiate the variables, in this case the u and the x like this du = 9 dx
phi
  • phi
and once you have du = 9 dx then you also have \[ dx = \frac{1}{9} du \]
phi
  • phi
now do your variable substitution replace 9x+2 with u replace dx with 1/9 du
phi
  • phi
and if we have limits, we would also change the limits.
phi
  • phi
and because it is easy to integrate a power, I would use the -8 exponent and get rid of the fraction
anonymous
  • anonymous
So would it be: \[63u ^{-8}*1/9 du\] ??
phi
  • phi
yes and the problem is \[ 7 \int u^{-8} du \] which you can do , right?
xapproachesinfinity
  • xapproachesinfinity
Yes
phi
  • phi
once you integrate, replace u with 9x+2 to put the answer in terms of x
SolomonZelman
  • SolomonZelman
\(\large\color{slate}{\displaystyle\int\limits_{~}^{~}\frac{63}{(9x+2)^8}~dx}\) \(\large\color{slate}{\displaystyle u=9x+2}\) \(\large\color{slate}{\displaystyle du=(9x+2)'~\cdot dx~~~\rightarrow~~~du=9~dx}\) (you already have a 9 and dx to replace that by du, just need to re-write it. \(\large\color{slate}{\displaystyle\int\limits_{~}^{~}\frac{7\cdot 9}{(9x+2)^8}~dx}\) \(\large\color{slate}{\displaystyle\int\limits_{~}^{~}\frac{7}{(9x+2)^8}~(9\cdot dx)}\) substitution:: \(\large\color{slate}{\displaystyle\int\limits_{~}^{~}\frac{7}{(u)^8}~(du)}\) and then all you have left:: \(\large\color{slate}{\displaystyle\int\limits_{~}^{~}7~u^{-8}~du}\)
SolomonZelman
  • SolomonZelman
(APPLY THE POWER RULE, AND don't forget to substitute the x back for u.)
SolomonZelman
  • SolomonZelman
igtg....
anonymous
  • anonymous
Ok, I got it! Thank you all!

Looking for something else?

Not the answer you are looking for? Search for more explanations.